Her remaining two shows, on November 14 and 15, will remain at the Powerstation.
Promoters blamed the move on "licensing complications".
Anyone holding all-ages tickets to Lorde's shows on November 14 and 15 are unable to go as the venue was R18, but they could use their tickets to get into her Bruce Mason Centre show on Sunday.
Promoters said they were "incredibly disappointed with this last-minute venue change".
On Friday afternoon Lorde vented her displeasure on Twitter, promising to make it up to fans and saying she was "blindsided" by the change.
Responding individually to some fans, she said management would send free merchandise to affected people, if they sent a photo of their ticket and booking information for verification.
"Not cool, I'm so bummed out," she wrote.
"If you can't make the Sunday show, reply to this and I'll hook you up with some special hometown merch on me."